APPLIED PHYSICS LETTERS
VOLUME 74, NUMBER 8
22 FEBRUARY 1999
Mechanics of rollable and foldable film-on-foil electronics
Z. Suoa)
Department of Mechanical and Aerospace Engineering and Princeton Materials Institute,
Princeton University, Princeton, New Jersey 08544
E. Y. Ma, H. Gleskova, and S. Wagner
Department of Electrical Engineering and Center for Photonics and Optoelectronic Materials,
Princeton University, Princeton, New Jersey 08544
~Received 27 October 1998; accepted for publication 21 December 1998!
The mechanics of film-on-foil devices is presented in the context of thin-film transistors on steel and
plastic foils. Provided the substrates are thin, such transistors function well after the foils are rolled
to small radii of curvature. When a substrate with a lower elastic modulus is used, smaller radii of
curvature can be achieved. Furthermore, when the transistors are placed in the neutral surface by
sandwiching between a substrate and an encapsulation layer, even smaller radii of curvature can be
attained. Transistor failure clearly shows when externally forced and thermally induced strains add
to, or subtract from, each other. © 1999 American Institute of Physics. @S0003-6951~99!03608-6#
film and the substrate have thicknesses d f and d s and
Young’s moduli Y f and Y s . When the sheet is bent, the top
surface is in tension, and the bottom surface is in compression. One surface inside the sheet, known as the neutral surface, has no strain. The strain in the top surface e top , in the
bending direction shown in Fig. 2, equals the distance from
the neutral surface divided by R. Typical silicon TFT materials and steel have about the same Young’s modulus. Consequently, the neutral surface is the midsurface of the sheet,
and the strain in the top surface is given by
The advent of active-matrix liquid-crystal displays has
opened the era of large-area electronics. Many anticipated
macroelectronic products, including x-ray sensors and digital
wallpaper, will be far bigger than today’s integrated circuits.
Their widespread use will depend on a low-cost per circuit
area rather than per circuit function. Part of this reduction
will come from low material consumption and new manufacturing technologies. For example, thin-film transistors
~TFTs! on thin foils1,2 use less materials per unit area, and
lend themselves to roll-to-roll fabrication. We show in this
letter that such devices can be made particularly rugged.
We fabricated TFTs on steel and polyimide foils. The
maximum substrate temperature was 350 °C for steel, and
150 °C for polyimide. All silicon-containing layers were
grown by plasma-enhanced chemical vapor deposition. First,
the substrate foil was coated with a 0.5 mm thick SiNx layer.
An ;100 nm thick Cr layer was evaporated and etched to
create the gate electrode. Then, the TFT stack of 360–400
nm of SiNx , ;200 nm undoped a-Si:H, and ;50 nm of
(n 1 ) a-Si:H were grown. An ;100 nm thick Cr layer was
evaporated and etched to form the source–drain pattern. Finally, the back channel into the (n 1 ) a-Si:H, the transistor
island, and the gate contact pads were defined by plasma
etching.
Figure 1 shows two transistor islands on a 25 mm thick
steel foil wrapped around a pencil. When the sheet was
rolled to drill bits of successively smaller radii of curvature,
the transistors functioned well until some critical radii were
reached: 2.5 mm if the transistors faced in, or 1.5 mm if the
transistors faced out. In both cases, failure was caused by the
delamination of the spin-on glass planarization layer from
the steel.
To appreciate these results, let us analyze the strain in a
blanket film deposited on a foil substrate. Both fabrication
process and externally applied bending moment cause strain
in the film. We first consider the external bending moment.
Figure 2 illustrates a sheet bent to a cylinder of radius R. The
e top5 ~ d f 1d s ! /2R.
The minimum allowable radius of curvature scales linearly
with the total thickness, assuming that the transistors fail
upon reaching a critical value of strain.
Now let us look at the TFT film on a more compliant
substrate such as plastic. The film and the substrate have
different elastic moduli (Y f .Y s ), so that the neutral surface
shifts from the midsurface and toward the film. Consequently, the strain on the top surface is reduced, as given by
e top5
S
D
d f 1d s ~ 112 h 1 x h 2 !
,
2R ~ 11 h !~ 11 x h !
~2!
where h 5d f /d s and x 5Y f /Y s . Figure 3 plots the normalized strain in the film versus h. Two kinds of substrates are
compared: steel (Y f /Y s >1) and plastic (Y f /Y s >100). For
given R and d f 1d s , the compliant substrate can reduce the
strain by as much as a factor of 5.
The strain in a circuit is further reduced if it is placed in
the neutral surface itself, sandwiched between the substrate
FIG. 1. A 25 mm thick steel foil wrapped around a pencil. Two transistor
islands on the foil are visible.
a!
Electronic mail: suo@princeton.edu
0003-6951/99/74(8)/1177/3/$15.00
~1!
1177
© 1999 American Institute of Physics
1178
Suo et al.
Appl. Phys. Lett., Vol. 74, No. 8, 22 February 1999
eralized plane strain. Let z be the through-thickness coordinate, whose origin is arbitrarily placed in the bottom surface.
Although the deflection is much larger than the sheet thickness, the strain typically is small. The geometry dictates that
the strain in the bending direction, e B , be linear in z, namely,
e B 5 e 0 1z/R,
FIG. 2. A film-on-foil structure bends into a cylindrical roll.
and an encapsulation layer of suitable Young’s modulus and
thickness Y e and d e . When the stiffness of the circuit proper
is negligible, the circuit comes to lie in the neutral surface if
Y s d 2s 5Y e d 2e .
~3!
In this case bending does not add any strain to the circuit.
Consequently, the bending curvature is no longer limited by
the failure strains of the transistor materials, but by those of
the substrate and the encapsulation. When low modulus,
small thickness substrate, and encapsulation are used, the
whole structure can be bent to extremely small radii. It can
even be folded like a map.
Next, we consider bending caused by the fabrication
process. During TFT fabrication, the substrate foil may be
held in a frame, at elevated temperatures. Upon cooling and
release from the frame, the structure often bends due to film
growth strain and differential thermal expansion. Several recent papers have adapted the classical theory of bimetallic
strips to integrated circuits on crystalline substrates.3–5 Here,
we present aspects specific to the film-on-foil structures. The
stress field due to misfit strains is biaxial in the surface of the
film and the substrate. A small, stiff wafer bends into a
spherical cap with an equal and biaxial curvature. However,
a film-on-foil structure bends into a cylindrical roll. The capto-roll transition as the substrate becomes thinner and larger
has been studied extensively.4 Our substrates are so compliant that they are on the ‘‘roll side,’’ far from the transition
point. Consequently, they are taken to bend into cylindrical
shape, as shown in Fig. 1.
The strain in the axial direction, e A , is independent of
the position throughout the sheet, a condition known as gen-
~4!
where e 0 is the strain at z50.
If the film and the substrate were separate, they would
strain by different amounts, but develop no stress. Let e be
the strain developed in a stress-free material. For example,
thermal expansion produces e5 a DT, where a is the thermal
expansion coefficient, and DT the temperature change. One
may also include in e the strain developed during film
growth. Because the film and the substrate are bonded and do
not slide relative to each other, a stress field arises. The two
stress components in the axial and the bending directions, s A
and s B , are both functions of z. Each layer of material is
taken to be an isotropic elastic solid with Young’s modulus Y
and Poisson’s ratio n. The film and the substrate are dissimilar materials, so that e, Y, and n are the known functions of z.
Hooke’s law relates the stresses to the strains as
S
S
D
D
S
S
D
D
s A5
e A1 e B
e A2 e B
Y
Y
2e 1
,
12 n
2
11 n
2
~5a!
s B5
e A1 e B
e A2 e B
Y
Y
2e 2
.
12 n
2
11 n
2
~5b!
Assume that no external forces are applied. The force
balance requires that
Es
A dz50,
Es
B dz50,
Es
~6!
B zdz50.
Inserting Eqs. ~4! and ~5! into Eq. ~6! and integrating, we
obtain three linear algebraic equations for the three constants
e A , e 0 , and 1/R. The procedure outlined here is applicable
to any number of layers, and arbitrary functions e(z), Y (z),
and n (z). The general solution can be developed, but is too
lengthy to list here. Instead, we consider two important special cases, assuming that Poisson’s ratio n is identical for the
film and the substrate.
Suppose that a film–substrate couple is bent by differential thermal expansion. The difference in the thermal strain is
e M 5( a f 2 a s )DT. For a stiff wafer, an equal and biaxial
stress arises in the plane of the film, which causes bending.
The radius of curvature R is given by the Stoney formula:3–5
R5
ds
.
6e M x h
~7!
When the substrate is thin and compliant, the film–
substrate couple bends into a cylindrical roll instead of a
spherical cap. Choose the origin of the z axis such that
* Y (z)zdz50. Substituting Eq. ~5! into the last equation in
Eq. ~6!, we can solve for the radius of curvature. The result is
R5
FIG. 3. Normalized strain in the film as a function of film/substrate thickness ratio. Two substrates are illustrated: steel (Y f /Y s >1) and plastic
(Y f /Y s >100).
F
GF
G
ds
~ 12 x h 2 ! 2 14 x h ~ 11 h ! 2
.
6 ~ 11 n ! e M x h
11 h
~8!
The term in the first bracket is the Stoney formula divided by
(11 n ), a factor arising from the generalized plane strain
condition. The term in the second bracket comes from the
Suo et al.
Appl. Phys. Lett., Vol. 74, No. 8, 22 February 1999
FIG. 4. Normalized radius of curvature as a function of film/substrate thickness ratio. Full lines are the solution for a cylindrical roll with n 50.3.
Dashed lines are the Stoney formula for a spherical cap formed by a thick,
stiff wafer.
effect of the compliant substrate. The radius of curvature,
calculated from Eqs. ~7! and ~8!, is plotted as a function of
d f /d s in Fig. 4. For typical TFT materials on a steel substrate, Y f /Y s >1, and the Stoney formula is a good approximation if d f /d s <0.1 and the (11 n ) factor is included. For
an organic substrate, Y f /Y s >100, and the Stoney formula is
useful only for d f /d s <0.001. In the specific case of a 50 mm
thick polyimide substrate, d f /d s >0.01, and Eq. ~8! must be
used.
We mentioned earlier that the transistors peel off the
steel substrate at a smaller radius of curvature when the transistors face out than when the transistors face in. This behavior arises from the way the misfit strain e M and the strain e top
induced by forced bending add. For our sample, differential
thermal expansion put the transistor material in compression,
1179
e M '4.531023 . ~We neglect any strain during film growth.!
Bending to a 1.5 mm radius adds a strain e top'8.531023 ,
tensile when the transistors face out, and compressive when
the transistors face in. Consequently, the net strain is 4
31023 tensile when the transistors face out, and 1331023
compressive when the transistors face in.
In summary, this letter gives the basic mechanics relations for externally forced and thermally induced bending of
the film-on-foil devices. When TFTs are placed on the surface of a foil substrate, the smallest bending radius is set by
the failure strain of the TFT materials. When the TFTs are
placed on a low elastic modulus substrate, the smallest bending radius can be reduced. Furthermore, when the TFTs are
placed in the neutral surface by sandwiching between the
substrate and the encapsulation, the smallest bending radius
is set by the failure strains of the substrate and the encapsulation materials. Consequently, extremely small radii of curvature can be achieved, which may open new applications of
large-area electronics.
This work is supported by DARPA ~N6001-98-1-8916!.
One of the authors ~Z.S.! is also grateful for the support of
the Institute for Materials Research and Engineering, Singapore.
1
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Wagner, Mater. Res. Soc. Symp. Proc. 507, 13 ~1998!.
2
H. Gleskova, S. Wagner, and Z. Suo, Mater. Res. Soc. Symp. Proc. 508,
73 ~1998!.
3
L. B. Freund, J. Mech. Phys. Solids 44, 723 ~1996!.
4
M. Finot, I. A. Blech, S. Suresh, and H. Fujimoto, J. Appl. Phys. 81, 2475
~1997!.
5
S. N. G. Chu, J. Electrochem. Soc. 145, 3621 ~1998!.